We next show that SVP satisfied the desired out-of-sample guarantee (REF ). We note that existing finite sample guarantees, c.f., [1]} and [2]} and Proposition REF  in this paper, do not directly imply the desired asymptotic guarantee (REF ) for SVP. A finer analysis will hence be required. Interestingly, our proof uses completely different techniques than [1]} and [2]}.
While their proofs rely on concentration inequalities on the empirical standard deviation, our proof uses the DRO form (REF ) of SVP combined with the Moderate Deviation Principle (Theorem REF ) from Large Deviation Theory.
